e to the i pi

[Lane Straatman]

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <complex.h>
/*
double complex z1, z2, z3;
bool flag;
z1 = .4 + .7I;
z2 = cpow(z1, 2.0);
z3 = z1 * z1;
flag = false;
flag = true;
if (flag)
{
printf("%lf %lf\n", creal(z1), cimag(z1));
printf("%lf %lf\n", creal(z2), cimag(z2));
printf("%lf %lf\n", creal(z3), cimag(z3));
printf("%d\n", N);
}
*/

int main(int argc, char *argv[])
{
double complex z1, z2, z3, z4, z5;
z1=5 +7I;
z2=cpow(z1, 1I);
printf("%lf %lf\n", creal(z1), cimag(z1));
printf("%lf %lf\n", creal(z2), cimag(z2));
z5= 0 + I*(3.14159);

z3=2.54 + 0*I;
z4=cpow(z5,z3);
printf("%lf %lf\n", creal(z4), cimag(z4));

system("PAUSE") ;
return 0;
}
Why doesn't e^(i *pi) equal what most folks think it does? LS

[Lane Straatman]

"Eric Sosman" <es*****@acm-dot-org.invalidwrot e in message
news:_8******** *************** *******@comcast .com...

Malcolm McLean wrote:

>"Lane Straatman" <in*****@invali d.netwrote in message

>>Why doesn't e^(i *pi) equal what most folks think it does? LS

Most folks would say that if you try to multiply a number by itself an
imaginary number of times, that is impossible.

That's plane wrong.

You're plain funny. LS

[Keith Thompson]

"Malcolm McLean" <re*******@btin ternet.comwrite s:

"Richard Heathfield" <rj*@see.sig.in validwrote in message

CBFalconer said:

Malcolm McLean wrote:
"Lane Straatman" <in*****@invali d.netwrote in message

Why doesn't e^(i *pi) equal what most folks think it does?

Most folks would say that if you try to multiply a number by
itself an imaginary number of times, that is impossible.

Not in the complex field.

Read again, more carefully. Malcolm is not talking about imaginary
arithmetic, but about what "most folks would say" about it. Most folks
don't know spit about mathematics.

If we multiply an imaginary number by itself an imaginary number of times,
maybe that would be real, on the analogy that a negative number multiplied
by itself is a positive.

No, that's not how it works. Operations on imaginary and complex
numbers are well defined mathematically, and well supported in C99.

Let's try it

int main(void)
{
int unity = 1;
int test1;

test1 = 0 - unity;

printf("%d * %d = %d\n", test1, test1, test1 * test1);
printf("Now a bit more complex %f\n", pow( sqrt(test1), sqrt(test1) );

return 0;
}

Nope.

Let me guess, you were so certain you were right that you didn't
bother to try it. There's a missing ')' on the second printf. You're
missing the required "#include <stdio.h>", which you can probably get
away with on many implementations . You're also missing the required
"#include <math.h>", which will probably cause the double results of
pow() and sqrt() to be interpreted as type int.

The sqrt() function takes a double argument and returns a double
result. In mathematical terms, it applies only to real numbers; it
can't give you a valid result for sqrt(-1). C99 supports imaginary
and complex numbers, as we've been discussing in this very thread.

Let's try it again:

#include <complex.h>
#include <math.h>
#include <stdio.h>
int main(void)
{
const double pi = 4 * atan(1.0);
const double complex result = cexp(I * pi);
printf("pi = %.10g\n", pi);
printf("result = %.10g + %.10g * I\n",
creal(result), cimag(result));
return 0;
}

Here's the output I get:

pi = 3.141592654
result = -1 + 1.224606354e-16 * I

It's not surprising that the result is inexact, since the value of pi
cannot be represented exactly.

--
Keith Thompson (The_Other_Keit h) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <* <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.

[Keith Thompson]

Richard Heathfield <rj*@see.sig.in validwrites:

Eric Sosman said:

Malcolm McLean wrote:

"Lane Straatman" <in*****@invali d.netwrote in message
Why doesn't e^(i *pi) equal what most folks think it does? LS

Most folks would say that if you try to multiply a number by itself an
imaginary number of times, that is impossible.

That's plane wrong.

Either you have a couple of axes to grind, or you're misreading what
Malcolm wrote, which rings true.

Yes, what Malcolm wrote about "what most folks think" is at least
plausible (though I suspect that most people who would ask what
e^(i*pi) is in the first place are likely to know the answer). It
wasn't entirely clear to me that Malcolm understands the issue
himself.

On the other hand, perhaps Malcolm's subtlety just escaped me, in
which case I'm duly embarrassed to have missed it.

The fact that I wrote the above *before* I got the "couple of axes"
joke makes this more likely. *Sigh*

--
Keith Thompson (The_Other_Keit h) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <* <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.

[Keith Thompson]

"Lane Straatman" <in*****@invali d.netwrites:
[...]

For kicks and giggles, I'd like to see how precise one can get with this
using these predefined types. arctan of 1.0 will improve pi. Is there an
easy way to adduce e in C to the full width of a double? LS

exp(1.0)

--
Keith Thompson (The_Other_Keit h) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <* <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.

[Malcolm McLean]

"Keith Thompson" <ks***@mib.orgw rote in message

Let me guess, you were so certain you were right that you didn't
bother to try it.

Microsoft have taken away my compiler. I bought a brand new Windows Vista
machine, installed my copy of Visual Studio and - no executable.

[Richard Heathfield]

Malcolm McLean said:

>
"Keith Thompson" <ks***@mib.orgw rote in message

>Let me guess, you were so certain you were right that you didn't
bother to try it.

Microsoft have taken away my compiler. I bought a brand new Windows Vista
machine, installed my copy of Visual Studio and - no executable.

You need Service Pack 7. Admittedly, Visual Studio won't work with that
either (possibly modulo emulators), but you get a perfectly capable C
compiler as part of the bundle. And of course it's completely free.

--
Richard Heathfield
"Usenet is a strange place" - dmr 29/7/1999
http://www.cpax.org.uk
email: rjh at the above domain, - www.

[Lane Straatman]

"jacob navia" <ja***@jacob.re mcomp.frwrote in message
news:45******** *************** @news.orange.fr ...

Lane Straatman a écrit :

>"Malcolm McLean" <re*******@btin ternet.comwrote in message
news:MK******* *************** ********@bt.com ...
[...]

>>>If we multiply an imaginary number by itself an imaginary number of
times, maybe that would be real, on the analogy that a negative number
multiplied by itself is a positive.

Let's try it
[commented out, below]
Nope.

I'm not sure what Malcolm is trying to do here. Without the overloading
of functions in tgmath.h, I doubt that sqrt() and pow() are going to
cover the complex cases. I couldn't get sqrt() to work on an imaginary.

Devcpp doesn't even have tgmath.h . I copied it out of lcc and put it in
the include file and got a cool 300 errors:

That will never work.

Sorry, header files are NOT portable

A lot of them are, but this is exactly the type that would not be: filled
with type definitions that ordinary mortals can't remember. sqrt() looks
like this in tgmath.h at the dinkumware site:
sqrt
double sqrt(double x);
float sqrt(float x);
long double sqrt(long double x);
double _Complex sqrt(double _Complex x);
float _Complex sqrt(float _Complex x);
long double _Complex sqrt(long double _Complex x);The function returns the
real square root of x, x^(1/2).

I would think double _Complex sqrt(double _Complex x) gives the root in the
complex plane we're looking for.

--

LS

center: "All the King's Men", perennial intramural basketball champs

[Malcolm McLean]

"Richard Heathfield" <rj*@see.sig.in validwrote in message

>Microsoft have taken away my compiler. I bought a brand new Windows Vista
machine, installed my copy of Visual Studio and - no executable.

You need Service Pack 7. Admittedly, Visual Studio won't work with that
either (possibly modulo emulators), but you get a perfectly capable C
compiler as part of the bundle. And of course it's completely free.

Seriously?
I need a Windows library to compile my games and BASICdraw, but not for
scientific stuff. At the moment I'm just glad I didn't throw my old PC away.
However I did put the old cathode ray monitor to one side, so now I have to
unplug and replug monitors every time I use my compiler.

They are up to service pack 7 within one week of the OS coming on market?

[Keith Thompson]

"Lane Straatman" <in*****@invali d.netwrites:
[...]

Is there something about tgmath.h that makes its inclusion here ill-advised?

Yes, it's not supported my many compilers, and you don't need it.
<tgmath.hjust lets you use simple names for math functions that work
with any real type. The declarations in <tgmath.hare "type-generic
macros" that simply invoke the appropriate function for the argument
type. For example, to compute the square root of a "double complex"
value, just use the csqrt() function in <complex.h(or csqrtf() for
"float complex", or csqrtl for "long double complex").

--
Keith Thompson (The_Other_Keit h) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <* <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.

[Richard Heathfield]

Malcolm McLean said:

>
"Richard Heathfield" <rj*@see.sig.in validwrote in message

>>Microsoft have taken away my compiler. I bought a brand new Windows Vista
machine, installed my copy of Visual Studio and - no executable.

You need Service Pack 7. Admittedly, Visual Studio won't work with that
either (possibly modulo emulators), but you get a perfectly capable C
compiler as part of the bundle. And of course it's completely free.

Seriously?

Er, no. Sorry, Malcolm, I thought you knew - "Service Pack 7" is the traditional
name for Linux when being recommended as a fix for a Windows-specific problem.

I need a Windows library to compile my games and BASICdraw,

You have just discovered that Microsoft aren't all that interested in supporting
"legacy software" (e.g. their own two-year-old compiler, if your account is
anything to go by). Have you considered porting your stuff to a more stable
platform?

--
Richard Heathfield
"Usenet is a strange place" - dmr 29/7/1999
http://www.cpax.org.uk
email: rjh at the above domain, - www.